Macroeconomic data suggest that the New Keynesian Phillips curve is quite flat - despite microeconomic evidence implying frequent price adjustments. While real rigidities may help to account for the conflicting evidence, we propose an alternative explanation: if price markup/cost-push shocks are persistent and negatively correlated with the labor share, the latter being a widely used measure for marginal costs, the estimated pass-through of measured marginal costs into inflation is limited, even if prices are fairly flexible. Using a standard New Keynesian model, we show that the GMM approach to the New Keynesian Phillips curve leads to inconsistent and upward biased estimates if cost-push shocks indeed are persistent. Monte Carlo experiments suggest that the bias is quite sizeable: we find average price durations estimated as high as 12 quarters, when the true value is about 2 quarters. Moreover, alternative estimators appear to be biased as well, while standard diagnostic tests fail to signal a misspecification of the model.